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Equation of state for the NaClH2OCO2 system: prediction of phase equilibria and volumetric properties
Geochimica
et Cosmochimica
Pergamon
Acra.Vol. 59, No. Copyright 0 Printed
14, pp. 2869-2882, 1995 Elsevier
Science
1995 Ltd
USA. All rightsreserved OOl6-7037/95 $9.50+ .OO
in the
00167037( 95)00182-4
Equation of state for the NaCl-H20-CO2 system: Prediction of phase equilibria and volumetric properties ZHENHAO DUAN, NANCY MBLLER,
and JOHN H. WEARE
Department of Chemistry, University of California, San Diego, La Jolla, CA 92093-0340, (Received
USA
August 9, 1994; accepted in revised form April 17, 1995)
Abstract-An equation of state (EOS) has been developed for the NaCI-HrO-CO2 system which consistently predicts various properties including PVTX, immiscibility or phase equilibria, solubilities, and activities with an accuracy close to that of experimental data from 300 to about IOCKPCr&d O-6000 bar with NaCl concentrations to about 30 wt% of NaCl (relative to NaCl + H20) or to about 50 wt% with less accuracy. The EOS predicts that excess volumes can be over 30% of the total volume under some T-P conditions. Adding NaCl to the HzO-CO2 system dramatically increases the T-P range of immiscibility. The immiscibility field is minimal around 400-500°C. Above or below this temperature, it expands for a constant pressure. A moderately saline brine can evolve into a very saline brine by phase separation at high temperatures. The presence of NaCl can substantially decrease the activity of Hz0 and increase that of CO*, thus affecting decarbonation and dehydration reactions. Compared to the EOS of Bowers and Helgeson (1983a), the EOS of this study is more reliable in the calculation of volumetric properties particularly in the low pressure range. In addition, BH EOS cannot predict phase equilibria. 1. INTRODUCTION
Brown and Lamb ( 1989) proposed “ideal geometrical” mixing of HZO-NaCl and COz. They linearly interpolate isochores between the endmember COr and the binary HrONaCl. This provides an approximate means for isochore calculations. However, there are large errors because the excess volume of mixing H20-NaCl and COz can be lo-30% of the total volume of the mixture. In addition, it is not possible to obtain other thermodynamic information (such as chemical potentials or phase behavior) from this method. The purpose of this study is to develop an EOS which can predict both volumetric properties and phase equilibria for the system NaCl-H20-CO2 up to high temperatures and high pressures. Recently Anderko and Pitzer ( 1993) successfully developed an EOS for the NaCl-Hz0 system based on the methods introduced by Dimitrelis and Rrausnitz ( 1986). This equation can predict both PVT properties and phase equilibria in this binary to high temperatures ( > 300°C). A comprehensive study of various EOS reveals that this approach gives the most accurate representation of salt-containing systems. In this study, the same approach is adopted for the NaCl-H20CO2 system. The resulting EOS consistently predicts various properties including phase equilibria (or immiscibilities), activities, and volumetric properties with an accuracy close to that of experiments. Since the EOS of this study treats NaCl as ion-pair molecule, it is not reliable for temperature below 3OO”C,where the dissociation of NaCl is substantial. We note that this work does not replace our earlier EOS (Duan et al., 1992a,b) for salt-free systems which is more accurate for temperatures below 350°C.
HzO, CO*, and NaCl are the most frequently encountered species in natural fluids. The knowledge of pressure-volume-temperature (PVT) properties, phase equilibria (or immiscibilities), and chemical potentials (or activities) is essential to the understanding of mechanisms of various geological processes. For example, the properties of systems as diverse as oil deposits (Alston et al., 1985), Mississippi-valley ore deposits (Hanor, 1979), porphyry ore deposits (Ramboz, 1979), circulating seafloor hydrothermal fluids ( Welhan and Craig, 1979; Bischoff, 1980), geothermal fluids (Truesdell, 1993), and metamorphic fluids (Crawford, 1981) may be controlled by fluid immiscibility. The presence of NaCl in fluids can substantially change their thermodynamic properties. For example, the addition of NaCl into the CO*-Hz0 system can greatly increase the T-P range of immiscibility. Above the critical temperature of Hz0 (374”C), there is no immiscibility for the binary HzO-C02. However, the immiscible field may exist well above this temperature if NaCl is added. Immiscibility has a profound impact on the transportation of many ore-forming elements (W. Hu et al., unpubl. data) in hydrothermal processes and geothermal venting. Understanding the properties of the NaCl-H20-CO2 system is also essential to the prediction of mixed volatile equilibria in metamorphic settings and to the interpretation of observations made on fluid inclusions. In addition, PVT properties have been extensively used in the interpretation of fluid inclusion data (Ramboz et al., 1985; Diamond, 1990). Prior to this work, the only equation of state (EOS) available for the NaCl-H20-CO2 system was that of Bowers and Helgeson ( 1983a). As reviewed by Brown and Lamb ( 1989), that EOS reproduces the data of Gehrig ( 1980) at moderate densities, but extrapolates poorly to higher density mixtures. Furthermore, it cannot predict phase behavior, which is a major limitation for geochemical applications. In order to calculate isochores of this system for fluid inclusion studies,
2. THE EQUATION OF STATE The form of an EOS is generally chosen on the basis of its ability to describe a system with accuracy over a range of the data used in the parameter adjustment. To improve extrapolation beyond the range of data, forms justified by approximate theoretical results (e.g., the virial equation, hard-sphere gas results, etc.) are usually selected. However, these forms can only yield qualitative results. In all cases, 2869
Z. Duan, N. Meller, and J. H. Weare
2870
(4
-2
T=300°C
Data by Zakirov(1984)
I
1 -5 I
q l
X(CO2)=0.3 x(CD2)=0.5
I
1800
P (bar)
-5
0
zoo0
4ciM
6ooo
P (bar) FIG. 1. Comparisons of experimental molar volumes in the binary COr-Hz0 as a function of pressure with the predictions of the EOS of this study (a) T = 300°C; (b) T = 400°C; (c) T = 500°C; (d) 7’ = 700°C.
accurate representations must contain parameters which are evaluated from experimental data. The parameters for endmembers are usually evaluated from pure system data. Then a mixing rule, which properly combines the endmember parameters, is developed to accurately re-
produce mixture data. There are a number of different kinds of EOS, each having strengths and weaknesses. For example, cubic EOS such as the Peng-Robinson’s equation (Skryjek and Vera, 1986) predicts phase equilibria well for nonaqueous systems, but provides poor pre-
Table 1. The Parameters for CQ
bco,
49.52
ac4
(3.86491553-2.36222839/Tr+3.5197785~-1.01456034fTr4).106
(a&0,
-4.1850846Oe+06+5.18786559e+05/Tr
(ad),
1.49548462e+07+1.40232739etO6.fTr
(aeAzo,
-3.04732284e.io7
Tr = TL304.2
2871
Equation of state in the system NaCI-H,O-CO?
-2
I
I 4ooo
2ooo
adO0
P (bar) 61
I
1 T=700°C
q
Tedheidc(1959) -6
0
3oao
6ooo
P (bar) RG.1. (Continued) with complex but treatable interactions such as a system of hard spheres and dipoles. The idealized system, called the reference system, is described quantitatively using some theory with well-defined assumptions. Corrections are then added to account for differences between the teal and the idealized systems. The corrections, called perturbations, arc empirical. For Hehnhoitx free energy this gives
dictions of volumetric properties. The EOS developed by Duan et al. ( 1992b) is accurate in the CH,-C4-H20 system over a large T-P range, but has difficulties in salt-bearing systems like the NaCIH,O-CO, system. In the approach of Anderko and Pitxer ( 1993) and Dimitrelis and Prausnitz ( 1986), the system is first idealized as composed of species
a = aRf + ap. Table 2. The Interaction Parameters for the Binary HsO-CQ 0.88868-1.7347e-04Ti4.038e-07 Ts
%j
1.41683554-7.02857143D-04T if T<773 K 7iijvlijj
sii, ,
fj&,
Qij,
qsj
1.03463-0.ooo2T if R773 K
I 1.0
s,
,
Q..
,
p-...
1.28262-7.32919762e-04T+3.5119047&-07 T* i and j represent Co, and HsO.
I I
(1)
For correlation and prediction of phase behavior of nonpolar systems, Dimitrelis and Prausnitz ( 1986) used a hard-sphere mixture as a reference system. Because NaCl and Hz0 arc strong polar molecules at high temperatures, Anderko and Pitzer ( 1993) added a term representing the dipolar hard sphere contribution (i.e., the difference of Helmholtx energy of dipolar hard spheres and that of simple hard spheres). We found that the use of the dipolar hard sphere term is essential to capture the behavior of the complex salt containing system. This leads to d = aM + adip + aPr.
(2)
The compressibility factor 2 can be derived from the Hehnholtx energy using the relation, Z = -u[CJ(a/RT)/&],.
(3)
2872
Z. Duan, N. Meller, and J. H. Weare
1
(b) 1000 (a)
700
c-NaCl=20wt%
a
A
600
T = 350% T = 300°C
500 6W
L+V 400
Iii e
/
E e
P
n 300
NaCl= 0
400
NaCl
E
f
0
200
100
0 0.1
0.2
0.3
0.4
0.5
0.6
I
I
I
I
I
0.1
0.2
0.3
0.4
0.5
Go*
4
xc02
FIG. 2. (a) Vapor-liquid coexistence in the COr-HrO and in the NaCl-H,O-COr systems at 300°C. The solid lines: EOS of this study; the symbols: experimental data by Todheide and Franck (1963) and Takenouchi and Kennedy (1965). (b) Vapor-liquid coexistence in the COr-HZ0 and in the NaCl-HrO-COr systems at 350°C. The solid lines and the symbols are the same as in (a).
It follows that
I_=l+(~-2),+(~-~+l)~2-~~3
(5)
9
(1 - r))3
(4) where 2.1. The Hard Sphere Contribution By comparison with experimental phase equilibria data from nonpolar systems, Dimitrelis and Rausnitx ( 1986) found that the equation for hard spheres developed by Boublik ( 1970) and Mansoori et al. ( 1971) is superior to that by Carnahan and Starling ( I %9). Therefore, this expression, which is good for both pure systems and mixtures of different radius hard spheres, is adopted for the hardsphere reference term.
D = i xioi , i-l
(6)
E = i
,
(7)
,
(8)
xp
is, F = f: x,o;
Table 3. The Interaction Parameters for the Binary NaCl-CQ
I
qj
-1.73355444+5.60408826e-03 T-2.70381422e-06 T2 1.41683554-7.02857143e-04 T ifT<773 K 1.03463 - 0.0002 T if T2773 K
&x-j
,
Qiii
,
%a
, qjiii
I
1.28262-7.32919762e-04 T+3.5119047&07
i and j represent NaCl and m.
T2
Equation of state in the system NaCI-HaO-CO2
2873
Comparison of the Data of Gehrig (1980) with Those of Bischoff (1991)
(19)
c c XiXj[(bf” + bj”)/2]3 7=
1 j
=-
TN,, F
4v
67J .
(9) (20)
In this expression, v is molar volume, b is the van der Waals covolume, and NA is Avogadro’s number. As can be seen, only one parameter bi for each species needs to be determined (by placing xi = 1 in Rqns. 8 and 9), because oi can be found from Eqns. 8 and 9. The value of bi is determined by fitting experimental data of endmember systems. 2.2. The Dipolar Contribution The expression for the dipolar hard-sphere Hehnholta energy developed by Stell et al. (1972, 1974) and Rushbrooke et al. (1973) and the mixing rule by Twu et al. (1975) and Gubbins and Twu ( 1978) are adopted for the dipolar contribution in the mixture system.
+ (I + c,1) + c*r$ + Cr$)(Q
(21)
bi is the endmember van der Waals covolume and is evaluated from experimental data. Fitting cf. the parameters of the 1*(n) and b(n) functions, to the results from the hard-sphere equations of Rushbrooke et al. (1973) yields: c, = 1.6054, ca = -4.4521, c) = 10.0368, q = 0.35147, c5 = -1.83943, and q = 5.95676. T]and pi in the above expressions are obtained by 17 =
$ =f
I
I
F C xi-+, ,=I
a, = 9
+ 2q9 + 3Q.92).
(22)
3
,-I
(10)
(23) where 0 is dipole moment, k is Boltzmann constant, and b can be calculated in Eqn. 22. Therefore, p is the only parameter to be determined by fitting to dipole moment measurements.
where (11)
2.3. The Perturbation Contribution
(12) (13)
The perturbation contribution accounts for effects which cannot be represented by the hard-sphere term and the dipole hard-sphere term. Anderko and Pitxer ( 1993) developed the following expression for the perturbation contribution of mixtures:
z+-~(~+~++$+y$ (14) where vii = b,14u, qp = b,/4v
= (b&&jjr)‘i3/4v,
b, = [(bf’3 + b;“)/2]‘, MS) = 1 + Cl9 + cd + c3q3.
. >
(24)
In this equation, the quantities n, ocb, adb*, and aeb3 are related to the second, third, fourth, and fifth virial coefficients. These parameters together with b are evaluated from endmember (pure system) experimental data and the following mixing rules:
(15) (25)
(16) (17)
(26)
(18)
Tabk 5. Ternary Interaction Parameters for tbe NaCl-H#-CGs
I-u
I
Qjt,EiiijL.Ei~~r+*bt~rbt~
i. j and k represent NaCl, HsO and CQ.
System
I -0.207+0.00227T-l .05le-06 T2 1.28262-7.32919762e-04T+3.51190476e-O7T2
I
2814
2. Duan, N. Msller, and J. H. Weare T-500% P&WOO bar
NaCl
-
T-500% P-1000 bar
NaCl
EO9 of this Study
~~~~Fr~~~
H20
40
20
CQ
T-600% P-l COObar
coz
H&
20
40
(ww
NaCl
co,
CO2 (wt%)
-
T-700% P-looobar
NaCl
EOS ot lhii Study
- - - - Experiment by Frantz al al. (1992)
Hz0
20
f
40
Hfi
20
40
COn(wt%)
co,
CO2(wt%)
FIG. 3. Comparison of experimental phase equilibria (measured by synthetic fluid inclusion method) in the ternary NaCI-H,O-C4 with the prediction of the EOS of this study. (a) 5OO”C,2000 bar; (b) SOOT, 1000 bar; (c) 6OO”C, 1000 bar; (d) 7OO“C,1000 bar).
biiu = [(bi”’
(27) bm
= [(bi”’
+ b;‘3 + b:” + b,‘“)/4]“,
+ b,f” + b:” + b;‘) + b:‘“)/S13, ati = (aiaj)“$,
(31) (32) (33)
The mixing parameters in Eqns. 25-28 are related to the endmember parameters by the following equations: b, = [(bf’3 + b;” + b:“)/3]‘,
(30)
(34)
(29) T=930°C P-7500
T-BOO%
NaCl
bar
NaCl A
P-2660 bar
Hz0
20
40
I
Hz0
-
40
20
60
EOS of this Study
- - - - Experiment
by Kolechikov
and Kdechikova
(1990)
FIG. 4. The prediction of immiscibility boundary in the ternary NaCI-H20-C@ at 800°C and 2000 bar.
-
EOS of this Study
----
Experiment
by Johnson
(1991)
FIG. 5. The prediction of immiscibility boundary (measured by synthetic fluid inclusion method) in the ternary NaCl-H20-C@ at 930°C and 7500 bar.
2875
Equation of state in the system NaCI-H20-CO2 T-660°C P-2000 bar
3.2. C02-HP0
NaCl
A
-
EOS of this Study
----
DatabyJoyceandHdloway
FIG. 6. Comparison of experimental immiscibility boundary (measured using hydrogen and oxygen buffer) in the ternary NaCl-H20Ct& at 850°C and 2000 bar with the prediction of the EOS of this study.
Cue),* = l(ae)i(ae)j(ae)~(oe),(aeL1"5ei/u,,
(35)
where aif,, yr, 6,, and tiiUn are interaction parameters which are evaluated from mixed system data.
3. EVALUATION OF EXPERIMENTAL AND PARAMETERIZATION
DATA
The system NaCl-H20-CO, includes three pure systems (NaCl, H20, and C02), three binaries (NaCl-H20, NaClCOz, and HzO-C02), and one ternary. The parameters for pure NaCl and Hz0 and the binary interaction parameters for NaCl-Hz0 mixtures are taken from Anderko and Pitzer ( 1993). The thermodynamic properties for pure CO* and COz-Hz0 are well predicted by the EOS of Duan et al. ( 1992a,b). However, the form of that EOS is different from that of the EOS presented here. Therefore, we need to evaluate the parameters for pure COz, the binary mixture interaction parameters for COz-H20 and NaCl-Ca, and the ternary interaction parameters for NaCl-H20-CO,. Because there is little experimental data on systems with NaCl concentrations larger than 25 wt% (relative to NaCl + HrO), where liquid + solid NaCl field lies, the EOS of this study does not include the prediction of halite solubility and may be less accurate for high NaCl concentration systems.
Many PVT and phase equilibria data for this binary system have been reported. These data have been reviewed by Duan et al. ( 1992b). It was found that most of the PK% data agree within about 5%. There was some deviations in the phase equilibrium data. The reported compositions of the coexisting vapor phase differ by as much as 16% between Takenouchi and Kennedy ( 1964) and Todheide and Franck ( 1963 ) . Recently, Sterner and Bodnar ( 1991) and Mather and Franck ( 1992) remeasured the equilibrium composition and found agreement of Todheide and Frank’s data. All the PMX data above 300°C listed in Table 3 of Duan et al. (1992b), plus the phase data by Todheide and Franck (1%3) and Mather and Franck ( 1992) are used in the evaluation of H20-CO2 binary interaction parameters (Table 2). With this parameterization, it is shown by Fig. 1 that the EOS of this study can predict volumes in this binary with maximum deviation of about 5%. This is about the same accuracy as the EOS of Duan et al. ( 1992b). Figure 2a,b shows that the EOS described here can also predict phase equilibria accurately except for the critical region. D. B. Joyce and J. G. Belencoe (pets. commun.) measured the activities of Hz0 in this binary from 400 to 700°C at 500 bar using a hydrogen and oxygen fugacity buffer. These measurements can be predicted by the EOS of this study within the error bars except at 400°C. This is similar to the performance of our earlier EOS (Duan et al., 1992b) for temperatures above 350°C. 3.3. NaCl-CO2 Solubilities of CO* in molten NaCl have been studied by Gjothiem et al. ( 1962) in the temperature range 850-950°C at a Cq pressure of 1 atm. At 850 and 9XPC, the solubilities of CO1 in NaCl are 4.6 X 10m6and 6.0 X lop6 moles of CO* per cm3 of solvent, respectively. It is very likely that the NaCl solubility in the Ca vapor phase is smaller. Thus, CO, and NaCl are almost immiscible in the T-Prange of the present study. However, the concentrations of both NaCl and CO* in T=7OO”C P=5000 bar
3.1. co2 CO2 has no permanent dipole moment, so h = 0 and GP = 0. The van der Waals covolume of CO,, b,, and u, UC, ad, ae in Eqn. 24 are found from the PVT data of CO*. These data were reviewed by Duan et al. ( 1992a). 1846 data points, covering a range of 300-1000°C and O-8000 bar were used in the evaluation on these parameters. All the datasets agree with each other within about O.l-0.5% for pressures below 3500 bar. Above 3500 bar the deviation between datasets can be as much as 2.5%. The parameters for this EOS are listed in Table 1. The fit to the data has an average error in volume of 1.2%. The maximum deviation of the fit is 4.1% at 3500 bar and 320°C.
Ha0
-
20
40
co2
EOS of this Study
.-.- Exparimentby Joyce and Holloway - - - - Schematicline drawnby Joyce and Holloway FIG. 7. Calculation of phase equilibria at 700°C and 5000 bar and comparison with experimental data (measured using hydrogen and oxygen buffer). The dashed line is a schematic immiscibility boundary drawn by Joyce and Holloway (1993).
2876
Z. Duan. N. Mdler, and J. H. Weare
(a)
@I
21300 2400
2400
1600
1900
F e a
2600
-z 8 a
1200
MO
400
500
500 T
700
1200
300
PC)
2OQO
300
*I_ / ,
P-
x- = 0.0669 xw =o.s677 xc.&
=0.0654
I
300
4m
500
600
700
900
T PC)
300
400
700
590
900
T&~
FIG. 8. (a)-(d) Comparison of experimental PV7X properties in the ternaryNaCl-HzO-Cq with prediction of the EOS of this study. Symbols: the experimental data of Gehrig (1980); The dashed line: the predicted phase boundary. Below this boundary is the liquid-vapor two phase field and above the boundary is the single fluid phase field, solid lines: isochores. CP stands for critical point. H,O-containing fluids can be very high and the interaction between them is not negligible. It follows that we have to evaluate the CO,-NaCl interaction parameters directly from the ternary data as discussed below. The parameters are listed in Table 3. Because there are few experiments on systems with NaCl concentrations larger than 23 wt%, we cannot assess the validity of our new EOS for highly saline ternary compositions. 3.4. N&l-l&O-C02 The most extensive PV7’X dataset for this ternary system, about 5000 experimental data points covering temperature range from about 200-560°C and pressure range from 0 to 3000 bar, has been reported by Gehrig ( 1980). Note that his
original data need 0.4-2.98 correction (depending on temperature) in volume because of thermal expansion of aparatus. Since this is the only comprehensive PV7X dataset in this T-P range, we can only roughly estimate its uncertainty. The binary HZO-NaCl density data reported by Gehrig (1980) agree with densities interpolated from data reported by Bodnar (1985) witbin about 4% for pressures above 1000 bar. For pressures below 1000 bar, the deviation of the Gehrig (1980) data from those of Bischoff (1980) is about 7% as indicated by Table 4. In addition to these data, Johnson ( 1992) measured isochore locations using synthetic fluid inclusions with .QQ ranging from 0.1-0.5 1 and relative salinities of 6-23.9 wt% around 7000 bar and 900°C. Besides the PV7X data, Takenouchi and Kennedy ( 1965) reported COz solubility data in NaCl aqueous solution from
Equation of state in the system NaCl-H20-CO2
2817
Table 6. Comparisonof experimentalmole volumes with EOS
T(K)
P(bar)
xNcl
XI&o
xcor
VOW
V(DMw)
v(exp)
=mH)
err@Mw)
733
416
.0193
.9789
.0018
40.53
57.94
61.14
-33.71
-5.23
133
435
.0191
.9688
.0121
42.45
56.19
57.88
-26.66
-2.92
713
406
.0186
9439
.0375
45.74
58.62
62.03
-26.26
-5.49
713
403
.0185
.9415
.0400
47.83
60.48
61.14
-21.77
-1.08
703
407
.0183
9303
.0514
44.89
55.31
58.08
-22.72
-4.17
733
517
.0183
9303
.0514
45.88
49.45
51.97
-11.71
-4.85
703
412
.0180
.9146
.0674
51.35
59.46
61.14
-16.02
-2.75
733
402
.0324
9463
.0213
48.22
66.20
66.24
-27.20
-.OS
743
457
.0324
.9463
.0213
44.31
56.30
56.05
-20.94
.45
713
400
.0317
.9252
.0431
44.97
58.56
57.06
-21.19
2.62
763
403
.0714
.9259
.0027
39.22
IO.96
71.33
-45.01
-.52
.8677
.0654
42.86
53.00
56.05
-23.53
-5.43
713
423
The volume are
0569
in cm3/mo1e. v(BH),v(DMW) are the mole volumes calulated by the EOS of
Bowers and Helgeson (1983a) and by the EOS of this study,respectively.v(exp) is experimental mole volume By Gehrig (1980). en=(vm
- v,,).Ioo/v,.
300 to 400°C. Recently, Kotelnikov and Kotelnikova ( 1990) and Frantz et al. ( 1992) measured immiscibilities using synthetic fluid inclusions. The data of Frantz et al. ( 1992) range from 500 to 700°C and 1000-3000 bar. Except for the diagram at 600°C and 3000 bar, all the others have sufficient data to delineate the immiscibility boundaries and tie lines. The data of Kotelnikov and Kotelnikova ( 1990) covers a temperature range from 400 to 800°C and pressure range from 1000 bar to 2000 bar. We were unable to delineate the phase boundaries from this dataset except in the cases of 600 and 800°C at 2000 bar. The boundaries of the immiscibility at these temperatures are consistent with those of Frantz et al. (1992). These two datasets provide important insights into the phase conditions of this system under high T-P conditions. Useful data were also reported by Joyce and Holloway ( 1993 ) . They measured the activity of water in the ternary system using fH2and fs buffers. Based on the measured equilibrium activity-composition relation, they drew tie lines at 850°C and 2000 bar.
There are ten ternary parameters (see Table 5) to be evaluated. If all the ternary interaction parameters are equal to 1.O, it implies that the ternary interactions are negligible, and the ternary properties can be predicted on the basis of the three binary systems. However, our test indicates that ternary interaction parameters are indispensable for the reliable prediction of either phase behavior or volumetric properties, no matter how the binary parameters are adjusted. It was found that all the &&‘s can be set equal to each other with little effect on fitting. This is also true for all the cijWm’s. Therefore, only three ternary parameters as a function of temperature (7 coefficients in total) (see Table 5) need to be adjusted. We evaluated the three ternary parameters based on the 2547 data points (calibrated) of Gehrig (1980), Takenouchi and Kennedy ( 1965). and Frantz et al. ( 1992). These data fall into the T-P range below 700°C and 3000 bar. In order to test the extrapolation of the EOS, we reserve the data of Johnson ( 1991), Joyce and Holloway ( 1993), and Kotelnikov and Kotelnikova ( 1990)) which cover T-Prange up to 950°C and
Table 7. Predictionof Molar Volume (cc/mole) at High Temperaturesand Pressures v(exp)’
v(EOs)*’
.1870
27.61
21.92
.2800
30.78
30.81
.4866
.4890
35.60
34.56
~5483
.2900
29.96
29.94
T(C)
p(b=)
x(NaCl)
x(Hz0)
938
1458
.0410
.7720
930
6600
.0352
.6848
924
6800
.0244
940
7400
.0617
x(Q)
* The exp&mcntal data arc from Johnson (1992) ** calculated mole volume (cm3/mo1e)by the BOS of this study.
Z. Duan, N. Msller, and J. H. Weare
2878
500
Table 8. The Excess Volume’ (cc/mole) TK)
P(bar)
V,,
V,
400
500
49.73
6.48
400
1000
34.89
1.35
400
zoo0
28.98
0.39
500
500
73.05
23.17
500
loo0
41.79
4.65
5Oo
zoo0
31.21
0.19
700
500
118.47
7.04
700
loo0
60.84
9.52
700
zoo0
38.00
2.4
700
5ooo
27.53
-0.08
Pz2000 bar
VW
450
I
* V,,=vhx -
O.~WWZ-~.~VN,CI-~,O
400
I
0:
D
I
0.1
0.2 xyo 3
0.3
0.4
FIG. 10. The P-Tboundaries for the reaction 3 dolomite + 2 quartz + Hz0 = talc + 3 calcite + 3C& in the absence of NaCl (dashed line) and with the addition of 0.1 mole fraction of NaCl (solid line).
7500 bar. As shown below, the EOS is valid over a much broader T-P range than the range for the parameter evaluation.
tithxt.~~h~~~=~.~
4. COMPARISON WITH EXPERIMENTAL DATA 1.0
The reliability and accuracy of an EOS must be determined by comparison with experimental data. Here, we demonstrate the capability of this EOS to predict both phase equilibria (or immiscibilities) and volumetric properties (PVTX) in the ternary system. Figure 2a,b compares the EOS calculation of the liquidvapor equilibria with experimental data at 300 and 350°C respectively. In this figure, the NaCl concentration is not shown on the vapor side because it is so small. The figure
0.6
0.2
0.4 Go
0.6
0.6
1.0
P = 1000 bar
660%
o-05i7cc-9 @I
xyo
.
0.4 XYO
0.6
1.0
1.0 0.6 0.6
a, 0.4
0.0
0.2
0.6
1.0
FIG. 9. (a)-(c) The activities of Hz0 and CO2 at high temperatures and pressures. The cross bars are the experimental measurements of Joyce and Holloway (1993). The curved solid lines are the calculation of this EOS. The diagonal solid lines represent ideal mixing.
FIG. 11. The phase diagram of the system NaCl-H,O-CQ at various temperatures and constant pressure of loo0 bar. The part below 300°C is calculated from the EOS of Duan et al. ( 1992b).
Equation of state in the system NaCI-H*O-CO2
clearly demonstrates that the predictions of this EOS are within experimental accuracy under the conditions shown except near the critical range. It is interesting to note from these figures that the extent of immiscibility can be considerably increased over that of the CO*-Hz0 binary by the addition of NaCl. The accuracy of this EOS in the prediction of phase equilibria (immiscibilities) is further shown by Figs. 3, 4, 5, 6, and 7. Figure 3 shows the close agreement of the prediction of phase coexistence measurements of Frantz et al. ( 1992). Figure 3a,b (see above) indicates that the immiscibility fields decrease with increasing pressure for a given temperature. The diagram at 800°C and 2000 bar of Kotelnikov and Kotelnikova ( 1990), given by Fig. 4, is well predicted by our EOS. Although we did not use any data above 700°C and 3000 bar in the parameterization, the immiscibility at 930°C and 7500 bar are. well predicted as compared with the synthetic fluid inclusion measurement by Johnson ( 1991) (see Fig. 5). The data of Johnson ( 1991) are not sufficient to determine the tie lines. The tie lines between vapor-liquid phase equilibrium established by Joyce and Holloway (1993) are shown in Figs. 6 and 7. We show very good agreement with their data at 850°C and 2000 bar (Fig. 6). In Fig. 7, the tie line measured by Joyce and Holloway ( 1993) is in general agreement with our EOS. However, the schematic phase boundary they drew shows a substantially larger immiscibility field. Their data appear to be insufficient to draw this boundary. Figure 8a-d displays the comparison of volumetric data with the EOS of this study for systems of various compositions. In these figures, the nearly straight lines are the predicted isochores, the dashed lines are predicted phase boundaries, and the solid dots are the experimental PVT data of Gehrig ( 1980). It can be seen that the EOS is very close to the experimental data (within an error of about 6-796 in volume) under various conditions. Table 6 indicates that the EOS of Bowers and Helgeson ( 1983a) has much larger errors. The errors in the low pressure range will lead to big errors in the evaluating fugacities or chemical potentials. Because NaCl is treated as ion-pair molecules in the EOS and it partially dissociates below 35O”C, the accuracy decreases slightly below 350°C. Although the parameters in this EOS are evaluated from data below 700°C and 3000 bar, the volume measurements over 920°C and 7000 bar of Johnson ( 1992) are accurately predicted (see Table 7). 5. PREDICTION OF PROPERExcess volumes, activities, isochores, and phase equilibria can be determined from the EOS. All these properties are important in the understanding of fluid behavior under various geological conditions.
2879
We have previously discussed the excess volume in the C&COz-H20 system (Duan et al., 1992b) and shown that it can be a large percentage of the total volume. In the NaCl-Hz0 system, the excess volume can be both very negative and positive. For example, at 400°C and 1000 bar, the excess volume of the system O.lNaCl + 0.9Hz0 is -47.9 cubic centimeter (cc) when the total volume is 23.1 cc. The accuracy of the ideal geometric mixing approach of Brown and Lamb ( 1989) can be assessed by calculating the excess volume defined as v:, = &niX- xc@&& - (1 - xcl&)+&cI-H~,
(37)
where vti, is the molar volume of the ternary mixed system and VN~CJ-H~ is molar volume of the binary under the same T-P condition and same xN&xHIO ratio. It can be seen from Table 8 that the excess volume amounts to about 7-30% of the total volume for pressures below 2000 bar, and about O5% for pressures above 2000 bar. This implies that the approach (see above) of Brown and Lamb ( 1989) may give approximate result for pressures above 2000 bar, but incorrect results for pressures below 2000 bar. 5.2. Activities The activity of a species
i is
U<=
defined as
Xf4i/$p,
(38)
where 4p is the fugacity coefficient of species i in its pure state. The equations for calculating fugacity coefficients are listed in the Appendix. Comparison of the calculated activities in the binary H20-CO2 with the data of Joyce and Holloway ( 1993). as shown in Fig. 9, indicates that our calculations are in good agreement with experimental data except at the waterrich end. The activity measurements in the ternary NaClH,O-CO* by Joyce and Holloway ( 1993) enabled them to draw a tie line between liquid and vapor phase equilibrium. This tie line is well predicted by our EOS as shown in Figs. 6 and 7. Note that the data of J + H were not used in the evaluation of the parameters. As stated before, adding NaCl in the H20-CO2 system can dramatically change the activities of both Hz0 and C02. For example, at 450°C and 2000 bar, the fugacity coefficients of Hz0 and CO* in the system 0.6H20 + 0.4C02 are 0.316 and 2.404, respectively. However, adding 0.1 mole fraction of NaCl and keeping the Hz0 to CO2 ratio constant, these fugacity coefficients change to 0.222 and 4.607, respectively. This change in activity has a substantial effect on alteration reactions. For example, consider the decarbonation and dehydration reaction: 3CaMg(COs)2(dolomite)
+ 4SiO,(quartz)
+ Hz0
= Mg&,O&OH)z(talc) 5.1. Excess Volume
+ 3CaCO,(calcite)
The excess volume is defined as: ” VU =
l&j,
-
x
XjVi.
(36)
+ 3C02
(39)
in the system CaO-MgO-SiOz-HzO-CO* (Bowers and Helgeson, 1983b). Adding 0.1 mole fraction NaCl relative to NaCl + Hz0 + CO*, the stability field of the minerals will shift substantially as shown in Fig. 10.
2. Duan, N. Mailer, and J. H. Weare
2880
5.3. Calculation of Isochores, Homogenization Temperatures, Pressures, and Immiscihilities Using microthennometric
technique together with Raman spectrometry analyses, it is possible to find out the total composition and total homogenization temperatures (Ramboz et al., 1985; Williams-Jones and Ferreira, 1989; Diamond, 1990). According to the composition analyzed, a constant composition diagram with phase relations and isochores can be calculated. This kind of diagram determines the homogenization pressures (internal pressure) for a given homogenization temperature. With the known temperature, pressure, and compoaitiuu, the volume can be calculated. Isochores can be. calct&ed as needed. Such calculations are illustrated by Fig. 8a-d. The curved dashed lines in these figures are phase boundaries. This boundary also represents hom~)genization T-P aye. P;bove this curve. the system is homogeneous. Below this curve, the fluid separates into liquid and vapor phase. The compositions of the liquid and vapor phase can be determined from the EOS. The end of these dashed lines should be close to critical region. The nearly straight lines are isochores. The immiscibility can be better illustrated by a three dimension phase diagram. Such a diagram can be calculated from the EOS. Figure 11 is a constant pressure diagram show-
ing the phase relations under varying temperatures. It can be seen that the immiscibility field is minimal around 400°C. Above or below this temperature the immiscibility field expands. The dashed line A-B connects the critical points of various temperatures. Above 640°C, there are no critical points. The dashed straight lines are tie-lines representing liquid-vapor coexistence. The tie lines indicate that very highly saline brines may result from phase separation under high temperatures. More details on the relationship between the immiscibility and mineralization will be discussed in a separate publication (Hu et al., 1995). thank Drs. A. Anderko, K. S. Pitzer, and John Wheeler for valuable discussions. This work has been supported by funds from the Department of Energy: DE-FGO7-931D13247, University Energy Research Group, Central Canada Potash, and Unocal Science and Technology Division. Drs. I.-M. Chou, M. Sterner, R. Bodnar, and M. McKibben are acknowledged for their constmctive reviews.
Acknowledgmenrs-We
C02-NaCI on phase relations: Equation of state for H,O-CO?NaCl fluids at high pressures and temperatures. Geochim. Cosmochim. Acta 41, 1241-3275.
Bowers T. S. and Helgeson H. C. (1983b) Calculation of the thermodynamic and geochemical consequences in the system HrOC02-NaCI on phase relations: Metamorphic equilibria at high pressures and temperatures. Amer. Mineml. 68, 1059- 1075. Brown P. E. and Lamb W. M. ( 1989) P-V-T properties of fluids in the system HZ0 -t CO* t NaCI: New graphical presentations and implications for fluid inclusion studies. Geochim. Cosmochim. Acia 53, 1209-1221.
Camahan N. F. and Starling K. E. ( 1969) Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51,635-636. Crawford M. L. ( 1981) Phase equilibria in aqueous fluid inclusions. Mineral. Assoc. Can. Short Course Handb. 6,75-
100.
Diamond L. W. ( 1990) Fhrid inclusion evidence for P-V-T-X evolution of hydrothermal solutions in late alpine gold-quartz veins at Rnr~cnn. V-1 d’Ayas, Northwest Italian Alps. Amer. J. Sci. 290, 912-958.
Dimitrelis D. and Prausnitz 1. M. ( 1986) Comparison of two hardsphere reference systems for perturbation theories for mixtures. Fluid Phase Equilibria
31, l-21.
Duan Z., Msller N., and Weare J. H. (1992a) An equation of state for the CH4-C02-H20 system: 1. Pure systems from 0 to 1000°C and 0 to 8000 bar. Geochim. Cosmochim. Acta S6,2605-2617. Duan Z., Meller N., and Weare 1. H. ( 1992b) An equation of state for the CI&-Ca-Hz0 system: Il. mixtures from 50 to 1000°C and from 0 to 1000 bar. Geochim. Cosmochim. Acta 56, 26192631.
Franck E. U. and Todheide K. (1959) Therm&he Eigenschaften Uberkristischer Mischungen von Kohlendioxyd und Wasser bis zu 750°C and 2000 bar. 2. Phys. Chem. Neue Forge 22,232-245. Frantz J. D., Popp R. K., and Hoering T. C. ( 1992 )The compositional limits of fluid immiscibility in the system HrO-NaCl-COr as determined with the use of synthetic fluid inclusions in conjunction with mass spectrometry. Chem. Geol. %,237-255. Gehrig M. ( 1980) Phasengleichgewichte und PVT-Daten terntier Mischungen aus Wasser, kohlendioxid und Natriumchlorid bis 3 kbar and 550°C. Doctorate dissertation, Univ. Karlsruhe. Giothiem K.. Heeaelund P.. Krohn C.. and Motznildi K. ( 1962) On -the solubihty :FCOr on molten halides. Andes. Acra Chem. S&d. 16,689-694. Gubbins K. E. and Twu C. H. (1978) Thermodynamics of polyatomic fluid mixtures-I. Theory. C/tern. Eng. Sci. 33, 863-878. Hanor J. S. ( 1979) The sedimentary genesis of hydrothermal fluids. In Geochemisrry of Hydrothermal Ore Deposits (ed. H. L. Barnes), pp. 137- 168. Wiley-Interscience. Johnson E. L. ( 1991) Experimentally determined limits for H20COz-NaCI immiscibility in granulites. Geology 19,925-928. Johnson E. L. ( 1992) An assessment of the accuracy of isochore location techniques for H,O-COr-NaCI fluids at granulite facies pressure-temperature conditions. Geochim. Cosmochim. Acra 56, 295-302.
Editorial
handling: M. A. McKibben
REFJZRENCES Alston R. B., Kokolis G. P., and James C. F. ( 1985) COr minimum miscibility pressure: A correlation of impure CO, streams and live oil system.Soc. Pet. J. 25,268-274. Anderko A. and Pitzer K. S. ( 1993) Equation of state representation of phase equilibria and volumetric properties of the system NaCIHz0 above 573 K. Geochim. Cosmochim. Acta 57, 1657- 1680. Bischoff J. L. ( 1980) Geothermal system at 21 “N, East Pacific Rise: Physical limits on geothermal fluid and role of adiabatic expansion. Science 207, 1465 - 1469.
Bodnar
R. 1. ( 1985) Pressure-volume-temperature-composition properties of tbe system HrO-NaCl at elevated temperatures and pressures. Ph.D. dissertation, Penn. State Univ. Boublik T. ( 1970) Hard sphere equation of state. J. Chem. Phys. 53, (PVTX)
47
I-472.
Bowers T. S. and Helgeson H. C. (1983a) Calculation of the thermodynamic and geochemical consequences in the system HzO-
Joyce D. B. and Holloway J. R. ( 1993) An experimental determination of the thermodynamic properties of HrO-COr-NaCI fluids at high temperatures and pressures. Geochim. Cosmochim. Acta 57,733-746.
Kotelnikov A. R. and Kotelnikova Z. A. ( 1990) Experimental study of phase state of the system HzO-CO*-NaCl by method of synthetic fluid inclusions in quartz. Geohhimiya N4,526-537. Mansoori G. A., Carnahan N. F., Starling K. E., and Leland T. W. ( 197 1) Equilibrium thermodynamic properties of the mixture of hard spheres. J. Chem. Phys. 54, 1523-1525. Mather A. E. and Franck E. U. ( 1992) Phase equilibria in the system carbon dioxide water at elevated pressures. J. Phys. Chem. 96, 6-8. Ramboz C. ( 1979) Fluid inclusion study of the copper mineralization in the Southwest Tintic District (Utah). Bull. Sot. Fr. Mineral. 102,622-632.
Ramboz C., Schnapper D., and Dubessy J. ( 1985) The P-v-T-X-f0~
evolution of H,O-Ca-CH&earing fluid in a wolframite vein: Reconstruction from fluid inclusion studies. Geochim. Cosmochim. Acra 49, 205-219.
Equation of state in the system NaCI-H20-CO2 Rushbrooke G. S., Stell G., and Heye J. S. (1973) Theory of polar fluids. I. Dipolar hard spheres. J. Mol. Phys. 26, 1199- 1215. Shmulovich K. I., Shmonov V. M., Mazur V. A., and Kalinichev A. G. ( 1980) P-V-T and activity concentration relations in the H,O-C@ system (homogeneous solutions). Geochem. Inrl. 17, 123-139. Skryjek R. and Vera J. H. ( 1986) An improved Peng-Robinson equation of state for pure compounds and mixtures. Canadian J. Chem. Eng. 64,323-333. Stell G., Rasaiab J. C., and Narang H. ( 1972) Thermodynamic perturbation theory for simple polar fluids I. J. Mol. Phys. 23, 3934%. Stell G., Rasaiah J. C., and Narang H. (1974) Thermodynamic perturbation theory for simple polar fluids, II. J. Mol. Phys. 27, l3931414. Sterner S. M. and Bodnar R. J. (1991) Synthetic Fluid Inclusions X: Experimental determination of P-V-T-X properties in the CO*Ha0 system to 6 kb and 700°C. Amer. J. Sci. 291, l-54. Takenouchi S. and Kennedy G. C. (1964) The binary system C02Hz0 at high temperature and pressures. Amer. J. Sci. 262, lO551074. Takenouchi S. and Kennedy G. C. ( 1965) The solubility of carbon dioxide in NaCl solutions at high temperatures and pressures. Amer. J. Sci. 263,445-454. Todheide K. and Franck E. U. ( 1%3) Das Zweiphasengebiet und die Kritische Kurve in System kohlendioxide-Wasser bis zu Dntcken von 3500 bar. 2. Phys. Chem. Neue Forge 37,387-401. Truesdell A. H. (1993) Gas and isotope geochemistry of Geysers steam. In Geothermal Reservoir Technology Research Program: Abstracts of Selected Research Projects, pp. 68-69. Twu C. H., Gubbins K. E., and Cray C. G. ( 1975) Excess thermodynamic properties for liquid mixtures of non-spherical molecules. J. Mol. Phys. 29,713-729. Welhan J. A. and Craig H. (1979) Methane and hydrogen in East Pacific Rise hydrothermal fluids. Geophy. Res. L&t. 6,829-83 1. Williams-Jones A. E. and Feneira D. R. ( 1989) Thermal metamorphism and H,O-CQ-NaCl immiscibility at Patapedia, Quebec: evidence from fluid inclusions. Contrib. Mineral. Petrol. 102, 247-254. Zakirov I. V. ( 1984) The P-V-T relations in the H20-CO* system at 300 and 400°C. Geochem. Intl. 21,13-20.
2881
(A5)
where
‘(2)
aE
+--+_-
aF ax,’
(A61
where D, E, and Fare given by Eqns. 6-9 and 3E9 7
-=-
a0
a $ > -=( aE
-=
3: (1 -9)
(A7)
(1 -T)’
3:’
3E2 FZ
++$ln(l-n),
+(l
(A81
aF
2E’r) 7
Z$ln(l
+(lAPPENDIX
a)?
ax,
aE
a0
CALCULATION OF FUGACITY COEFFICIENTS
ax,= aE
A few errors in the equations of Anderko and Pitzer ( 1993) are corrected here. The fugacity coefficient Qi is given by:
ui*
-r)).
(A9) (AlO)
2
ax,=aF -&=u:.
(AlI
(A121
The dipolar contribution is given by where (pi- pj. ) is the difference between the chemical potential of component i in the real system and that in the ideal gas state. It is given by the sum of the hard-sphere, dipolar, and perturbation con-
Ac(idip_ RT
(A131
(AZ) The derivatives of A2 and A, with respect to the number of moles of component i are
The hard-sphere contribution is expressed as
+z-
ahd FT =
3DE Ff)-F 1-r)
E’
E’ Fz +(l+
1,
(A3)
9),
(A4)
2. Duan, N. Msller, and J. H. Weare
2882 where
x (1 +
Cd?) +
--1 a(n*u) = 2 i xja,, n 84 j_,
cg)* + C6TjJ)
+ (1 + c,q + cg2 + c&Cc,
+ 2~5~ + 3c.&l,
(A17)
n
X Xjby
acns, ,-I -=ani
2v
’
where b, is defined by Eqn. 17. The perturbation contribution to the chemical potential is
(A181
1 B(n%cb) --= n2 Chi
3 i
i
xj-G(ac)&ijk~
(A2’3)
(AZ])
j-l t-l
(A22)
et Cosmochimica
Pergamon
Acra.Vol. 59, No. Copyright 0 Printed
14, pp. 2869-2882, 1995 Elsevier
Science
1995 Ltd
USA. All rightsreserved OOl6-7037/95 $9.50+ .OO
in the
00167037( 95)00182-4
Equation of state for the NaCl-H20-CO2 system: Prediction of phase equilibria and volumetric properties ZHENHAO DUAN, NANCY MBLLER,
and JOHN H. WEARE
Department of Chemistry, University of California, San Diego, La Jolla, CA 92093-0340, (Received
USA
August 9, 1994; accepted in revised form April 17, 1995)
Abstract-An equation of state (EOS) has been developed for the NaCI-HrO-CO2 system which consistently predicts various properties including PVTX, immiscibility or phase equilibria, solubilities, and activities with an accuracy close to that of experimental data from 300 to about IOCKPCr&d O-6000 bar with NaCl concentrations to about 30 wt% of NaCl (relative to NaCl + H20) or to about 50 wt% with less accuracy. The EOS predicts that excess volumes can be over 30% of the total volume under some T-P conditions. Adding NaCl to the HzO-CO2 system dramatically increases the T-P range of immiscibility. The immiscibility field is minimal around 400-500°C. Above or below this temperature, it expands for a constant pressure. A moderately saline brine can evolve into a very saline brine by phase separation at high temperatures. The presence of NaCl can substantially decrease the activity of Hz0 and increase that of CO*, thus affecting decarbonation and dehydration reactions. Compared to the EOS of Bowers and Helgeson (1983a), the EOS of this study is more reliable in the calculation of volumetric properties particularly in the low pressure range. In addition, BH EOS cannot predict phase equilibria. 1. INTRODUCTION
Brown and Lamb ( 1989) proposed “ideal geometrical” mixing of HZO-NaCl and COz. They linearly interpolate isochores between the endmember COr and the binary HrONaCl. This provides an approximate means for isochore calculations. However, there are large errors because the excess volume of mixing H20-NaCl and COz can be lo-30% of the total volume of the mixture. In addition, it is not possible to obtain other thermodynamic information (such as chemical potentials or phase behavior) from this method. The purpose of this study is to develop an EOS which can predict both volumetric properties and phase equilibria for the system NaCl-H20-CO2 up to high temperatures and high pressures. Recently Anderko and Pitzer ( 1993) successfully developed an EOS for the NaCl-Hz0 system based on the methods introduced by Dimitrelis and Rrausnitz ( 1986). This equation can predict both PVT properties and phase equilibria in this binary to high temperatures ( > 300°C). A comprehensive study of various EOS reveals that this approach gives the most accurate representation of salt-containing systems. In this study, the same approach is adopted for the NaCl-H20CO2 system. The resulting EOS consistently predicts various properties including phase equilibria (or immiscibilities), activities, and volumetric properties with an accuracy close to that of experiments. Since the EOS of this study treats NaCl as ion-pair molecule, it is not reliable for temperature below 3OO”C,where the dissociation of NaCl is substantial. We note that this work does not replace our earlier EOS (Duan et al., 1992a,b) for salt-free systems which is more accurate for temperatures below 350°C.
HzO, CO*, and NaCl are the most frequently encountered species in natural fluids. The knowledge of pressure-volume-temperature (PVT) properties, phase equilibria (or immiscibilities), and chemical potentials (or activities) is essential to the understanding of mechanisms of various geological processes. For example, the properties of systems as diverse as oil deposits (Alston et al., 1985), Mississippi-valley ore deposits (Hanor, 1979), porphyry ore deposits (Ramboz, 1979), circulating seafloor hydrothermal fluids ( Welhan and Craig, 1979; Bischoff, 1980), geothermal fluids (Truesdell, 1993), and metamorphic fluids (Crawford, 1981) may be controlled by fluid immiscibility. The presence of NaCl in fluids can substantially change their thermodynamic properties. For example, the addition of NaCl into the CO*-Hz0 system can greatly increase the T-P range of immiscibility. Above the critical temperature of Hz0 (374”C), there is no immiscibility for the binary HzO-C02. However, the immiscible field may exist well above this temperature if NaCl is added. Immiscibility has a profound impact on the transportation of many ore-forming elements (W. Hu et al., unpubl. data) in hydrothermal processes and geothermal venting. Understanding the properties of the NaCl-H20-CO2 system is also essential to the prediction of mixed volatile equilibria in metamorphic settings and to the interpretation of observations made on fluid inclusions. In addition, PVT properties have been extensively used in the interpretation of fluid inclusion data (Ramboz et al., 1985; Diamond, 1990). Prior to this work, the only equation of state (EOS) available for the NaCl-H20-CO2 system was that of Bowers and Helgeson ( 1983a). As reviewed by Brown and Lamb ( 1989), that EOS reproduces the data of Gehrig ( 1980) at moderate densities, but extrapolates poorly to higher density mixtures. Furthermore, it cannot predict phase behavior, which is a major limitation for geochemical applications. In order to calculate isochores of this system for fluid inclusion studies,
2. THE EQUATION OF STATE The form of an EOS is generally chosen on the basis of its ability to describe a system with accuracy over a range of the data used in the parameter adjustment. To improve extrapolation beyond the range of data, forms justified by approximate theoretical results (e.g., the virial equation, hard-sphere gas results, etc.) are usually selected. However, these forms can only yield qualitative results. In all cases, 2869
Z. Duan, N. Meller, and J. H. Weare
2870
(4
-2
T=300°C
Data by Zakirov(1984)
I
1 -5 I
q l
X(CO2)=0.3 x(CD2)=0.5
I
1800
P (bar)
-5
0
zoo0
4ciM
6ooo
P (bar) FIG. 1. Comparisons of experimental molar volumes in the binary COr-Hz0 as a function of pressure with the predictions of the EOS of this study (a) T = 300°C; (b) T = 400°C; (c) T = 500°C; (d) 7’ = 700°C.
accurate representations must contain parameters which are evaluated from experimental data. The parameters for endmembers are usually evaluated from pure system data. Then a mixing rule, which properly combines the endmember parameters, is developed to accurately re-
produce mixture data. There are a number of different kinds of EOS, each having strengths and weaknesses. For example, cubic EOS such as the Peng-Robinson’s equation (Skryjek and Vera, 1986) predicts phase equilibria well for nonaqueous systems, but provides poor pre-
Table 1. The Parameters for CQ
bco,
49.52
ac4
(3.86491553-2.36222839/Tr+3.5197785~-1.01456034fTr4).106
(a&0,
-4.1850846Oe+06+5.18786559e+05/Tr
(ad),
1.49548462e+07+1.40232739etO6.fTr
(aeAzo,
-3.04732284e.io7
Tr = TL304.2
2871
Equation of state in the system NaCI-H,O-CO?
-2
I
I 4ooo
2ooo
adO0
P (bar) 61
I
1 T=700°C
q
Tedheidc(1959) -6
0
3oao
6ooo
P (bar) RG.1. (Continued) with complex but treatable interactions such as a system of hard spheres and dipoles. The idealized system, called the reference system, is described quantitatively using some theory with well-defined assumptions. Corrections are then added to account for differences between the teal and the idealized systems. The corrections, called perturbations, arc empirical. For Hehnhoitx free energy this gives
dictions of volumetric properties. The EOS developed by Duan et al. ( 1992b) is accurate in the CH,-C4-H20 system over a large T-P range, but has difficulties in salt-bearing systems like the NaCIH,O-CO, system. In the approach of Anderko and Pitxer ( 1993) and Dimitrelis and Prausnitz ( 1986), the system is first idealized as composed of species
a = aRf + ap. Table 2. The Interaction Parameters for the Binary HsO-CQ 0.88868-1.7347e-04Ti4.038e-07 Ts
%j
1.41683554-7.02857143D-04T if T<773 K 7iijvlijj
sii, ,
fj&,
Qij,
qsj
1.03463-0.ooo2T if R773 K
I 1.0
s,
,
Q..
,
p-...
1.28262-7.32919762e-04T+3.5119047&-07 T* i and j represent Co, and HsO.
I I
(1)
For correlation and prediction of phase behavior of nonpolar systems, Dimitrelis and Prausnitz ( 1986) used a hard-sphere mixture as a reference system. Because NaCl and Hz0 arc strong polar molecules at high temperatures, Anderko and Pitzer ( 1993) added a term representing the dipolar hard sphere contribution (i.e., the difference of Helmholtx energy of dipolar hard spheres and that of simple hard spheres). We found that the use of the dipolar hard sphere term is essential to capture the behavior of the complex salt containing system. This leads to d = aM + adip + aPr.
(2)
The compressibility factor 2 can be derived from the Hehnholtx energy using the relation, Z = -u[CJ(a/RT)/&],.
(3)
2872
Z. Duan, N. Meller, and J. H. Weare
1
(b) 1000 (a)
700
c-NaCl=20wt%
a
A
600
T = 350% T = 300°C
500 6W
L+V 400
Iii e
/
E e
P
n 300
NaCl= 0
400
NaCl
E
f
0
200
100
0 0.1
0.2
0.3
0.4
0.5
0.6
I
I
I
I
I
0.1
0.2
0.3
0.4
0.5
Go*
4
xc02
FIG. 2. (a) Vapor-liquid coexistence in the COr-HrO and in the NaCl-H,O-COr systems at 300°C. The solid lines: EOS of this study; the symbols: experimental data by Todheide and Franck (1963) and Takenouchi and Kennedy (1965). (b) Vapor-liquid coexistence in the COr-HZ0 and in the NaCl-HrO-COr systems at 350°C. The solid lines and the symbols are the same as in (a).
It follows that
I_=l+(~-2),+(~-~+l)~2-~~3
(5)
9
(1 - r))3
(4) where 2.1. The Hard Sphere Contribution By comparison with experimental phase equilibria data from nonpolar systems, Dimitrelis and Rausnitx ( 1986) found that the equation for hard spheres developed by Boublik ( 1970) and Mansoori et al. ( 1971) is superior to that by Carnahan and Starling ( I %9). Therefore, this expression, which is good for both pure systems and mixtures of different radius hard spheres, is adopted for the hardsphere reference term.
D = i xioi , i-l
(6)
E = i
,
(7)
,
(8)
xp
is, F = f: x,o;
Table 3. The Interaction Parameters for the Binary NaCl-CQ
I
qj
-1.73355444+5.60408826e-03 T-2.70381422e-06 T2 1.41683554-7.02857143e-04 T ifT<773 K 1.03463 - 0.0002 T if T2773 K
&x-j
,
Qiii
,
%a
, qjiii
I
1.28262-7.32919762e-04 T+3.5119047&07
i and j represent NaCl and m.
T2
Equation of state in the system NaCI-HaO-CO2
2873
Comparison of the Data of Gehrig (1980) with Those of Bischoff (1991)
(19)
c c XiXj[(bf” + bj”)/2]3 7=
1 j
=-
TN,, F
4v
67J .
(9) (20)
In this expression, v is molar volume, b is the van der Waals covolume, and NA is Avogadro’s number. As can be seen, only one parameter bi for each species needs to be determined (by placing xi = 1 in Rqns. 8 and 9), because oi can be found from Eqns. 8 and 9. The value of bi is determined by fitting experimental data of endmember systems. 2.2. The Dipolar Contribution The expression for the dipolar hard-sphere Hehnholta energy developed by Stell et al. (1972, 1974) and Rushbrooke et al. (1973) and the mixing rule by Twu et al. (1975) and Gubbins and Twu ( 1978) are adopted for the dipolar contribution in the mixture system.
+ (I + c,1) + c*r$ + Cr$)(Q
(21)
bi is the endmember van der Waals covolume and is evaluated from experimental data. Fitting cf. the parameters of the 1*(n) and b(n) functions, to the results from the hard-sphere equations of Rushbrooke et al. (1973) yields: c, = 1.6054, ca = -4.4521, c) = 10.0368, q = 0.35147, c5 = -1.83943, and q = 5.95676. T]and pi in the above expressions are obtained by 17 =
$ =f
I
I
F C xi-+, ,=I
a, = 9
+ 2q9 + 3Q.92).
(22)
3
,-I
(10)
(23) where 0 is dipole moment, k is Boltzmann constant, and b can be calculated in Eqn. 22. Therefore, p is the only parameter to be determined by fitting to dipole moment measurements.
where (11)
2.3. The Perturbation Contribution
(12) (13)
The perturbation contribution accounts for effects which cannot be represented by the hard-sphere term and the dipole hard-sphere term. Anderko and Pitxer ( 1993) developed the following expression for the perturbation contribution of mixtures:
z+-~(~+~++$+y$ (14) where vii = b,14u, qp = b,/4v
= (b&&jjr)‘i3/4v,
b, = [(bf’3 + b;“)/2]‘, MS) = 1 + Cl9 + cd + c3q3.
. >
(24)
In this equation, the quantities n, ocb, adb*, and aeb3 are related to the second, third, fourth, and fifth virial coefficients. These parameters together with b are evaluated from endmember (pure system) experimental data and the following mixing rules:
(15) (25)
(16) (17)
(26)
(18)
Tabk 5. Ternary Interaction Parameters for tbe NaCl-H#-CGs
I-u
I
Qjt,EiiijL.Ei~~r+*bt~rbt~
i. j and k represent NaCl, HsO and CQ.
System
I -0.207+0.00227T-l .05le-06 T2 1.28262-7.32919762e-04T+3.51190476e-O7T2
I
2814
2. Duan, N. Msller, and J. H. Weare T-500% P&WOO bar
NaCl
-
T-500% P-1000 bar
NaCl
EO9 of this Study
~~~~Fr~~~
H20
40
20
CQ
T-600% P-l COObar
coz
H&
20
40
(ww
NaCl
co,
CO2 (wt%)
-
T-700% P-looobar
NaCl
EOS ot lhii Study
- - - - Experiment by Frantz al al. (1992)
Hz0
20
f
40
Hfi
20
40
COn(wt%)
co,
CO2(wt%)
FIG. 3. Comparison of experimental phase equilibria (measured by synthetic fluid inclusion method) in the ternary NaCI-H,O-C4 with the prediction of the EOS of this study. (a) 5OO”C,2000 bar; (b) SOOT, 1000 bar; (c) 6OO”C, 1000 bar; (d) 7OO“C,1000 bar).
biiu = [(bi”’
(27) bm
= [(bi”’
+ b;‘3 + b:” + b,‘“)/4]“,
+ b,f” + b:” + b;‘) + b:‘“)/S13, ati = (aiaj)“$,
(31) (32) (33)
The mixing parameters in Eqns. 25-28 are related to the endmember parameters by the following equations: b, = [(bf’3 + b;” + b:“)/3]‘,
(30)
(34)
(29) T=930°C P-7500
T-BOO%
NaCl
bar
NaCl A
P-2660 bar
Hz0
20
40
I
Hz0
-
40
20
60
EOS of this Study
- - - - Experiment
by Kolechikov
and Kdechikova
(1990)
FIG. 4. The prediction of immiscibility boundary in the ternary NaCI-H20-C@ at 800°C and 2000 bar.
-
EOS of this Study
----
Experiment
by Johnson
(1991)
FIG. 5. The prediction of immiscibility boundary (measured by synthetic fluid inclusion method) in the ternary NaCl-H20-C@ at 930°C and 7500 bar.
2875
Equation of state in the system NaCI-H20-CO2 T-660°C P-2000 bar
3.2. C02-HP0
NaCl
A
-
EOS of this Study
----
DatabyJoyceandHdloway
FIG. 6. Comparison of experimental immiscibility boundary (measured using hydrogen and oxygen buffer) in the ternary NaCl-H20Ct& at 850°C and 2000 bar with the prediction of the EOS of this study.
Cue),* = l(ae)i(ae)j(ae)~(oe),(aeL1"5ei/u,,
(35)
where aif,, yr, 6,, and tiiUn are interaction parameters which are evaluated from mixed system data.
3. EVALUATION OF EXPERIMENTAL AND PARAMETERIZATION
DATA
The system NaCl-H20-CO, includes three pure systems (NaCl, H20, and C02), three binaries (NaCl-H20, NaClCOz, and HzO-C02), and one ternary. The parameters for pure NaCl and Hz0 and the binary interaction parameters for NaCl-Hz0 mixtures are taken from Anderko and Pitzer ( 1993). The thermodynamic properties for pure CO* and COz-Hz0 are well predicted by the EOS of Duan et al. ( 1992a,b). However, the form of that EOS is different from that of the EOS presented here. Therefore, we need to evaluate the parameters for pure COz, the binary mixture interaction parameters for COz-H20 and NaCl-Ca, and the ternary interaction parameters for NaCl-H20-CO,. Because there is little experimental data on systems with NaCl concentrations larger than 25 wt% (relative to NaCl + HrO), where liquid + solid NaCl field lies, the EOS of this study does not include the prediction of halite solubility and may be less accurate for high NaCl concentration systems.
Many PVT and phase equilibria data for this binary system have been reported. These data have been reviewed by Duan et al. ( 1992b). It was found that most of the PK% data agree within about 5%. There was some deviations in the phase equilibrium data. The reported compositions of the coexisting vapor phase differ by as much as 16% between Takenouchi and Kennedy ( 1964) and Todheide and Franck ( 1963 ) . Recently, Sterner and Bodnar ( 1991) and Mather and Franck ( 1992) remeasured the equilibrium composition and found agreement of Todheide and Frank’s data. All the PMX data above 300°C listed in Table 3 of Duan et al. (1992b), plus the phase data by Todheide and Franck (1%3) and Mather and Franck ( 1992) are used in the evaluation of H20-CO2 binary interaction parameters (Table 2). With this parameterization, it is shown by Fig. 1 that the EOS of this study can predict volumes in this binary with maximum deviation of about 5%. This is about the same accuracy as the EOS of Duan et al. ( 1992b). Figure 2a,b shows that the EOS described here can also predict phase equilibria accurately except for the critical region. D. B. Joyce and J. G. Belencoe (pets. commun.) measured the activities of Hz0 in this binary from 400 to 700°C at 500 bar using a hydrogen and oxygen fugacity buffer. These measurements can be predicted by the EOS of this study within the error bars except at 400°C. This is similar to the performance of our earlier EOS (Duan et al., 1992b) for temperatures above 350°C. 3.3. NaCl-CO2 Solubilities of CO* in molten NaCl have been studied by Gjothiem et al. ( 1962) in the temperature range 850-950°C at a Cq pressure of 1 atm. At 850 and 9XPC, the solubilities of CO1 in NaCl are 4.6 X 10m6and 6.0 X lop6 moles of CO* per cm3 of solvent, respectively. It is very likely that the NaCl solubility in the Ca vapor phase is smaller. Thus, CO, and NaCl are almost immiscible in the T-Prange of the present study. However, the concentrations of both NaCl and CO* in T=7OO”C P=5000 bar
3.1. co2 CO2 has no permanent dipole moment, so h = 0 and GP = 0. The van der Waals covolume of CO,, b,, and u, UC, ad, ae in Eqn. 24 are found from the PVT data of CO*. These data were reviewed by Duan et al. ( 1992a). 1846 data points, covering a range of 300-1000°C and O-8000 bar were used in the evaluation on these parameters. All the datasets agree with each other within about O.l-0.5% for pressures below 3500 bar. Above 3500 bar the deviation between datasets can be as much as 2.5%. The parameters for this EOS are listed in Table 1. The fit to the data has an average error in volume of 1.2%. The maximum deviation of the fit is 4.1% at 3500 bar and 320°C.
Ha0
-
20
40
co2
EOS of this Study
.-.- Exparimentby Joyce and Holloway - - - - Schematicline drawnby Joyce and Holloway FIG. 7. Calculation of phase equilibria at 700°C and 5000 bar and comparison with experimental data (measured using hydrogen and oxygen buffer). The dashed line is a schematic immiscibility boundary drawn by Joyce and Holloway (1993).
2876
Z. Duan. N. Mdler, and J. H. Weare
(a)
@I
21300 2400
2400
1600
1900
F e a
2600
-z 8 a
1200
MO
400
500
500 T
700
1200
300
PC)
2OQO
300
*I_ / ,
P-
x- = 0.0669 xw =o.s677 xc.&
=0.0654
I
300
4m
500
600
700
900
T PC)
300
400
700
590
900
T&~
FIG. 8. (a)-(d) Comparison of experimental PV7X properties in the ternaryNaCl-HzO-Cq with prediction of the EOS of this study. Symbols: the experimental data of Gehrig (1980); The dashed line: the predicted phase boundary. Below this boundary is the liquid-vapor two phase field and above the boundary is the single fluid phase field, solid lines: isochores. CP stands for critical point. H,O-containing fluids can be very high and the interaction between them is not negligible. It follows that we have to evaluate the CO,-NaCl interaction parameters directly from the ternary data as discussed below. The parameters are listed in Table 3. Because there are few experiments on systems with NaCl concentrations larger than 23 wt%, we cannot assess the validity of our new EOS for highly saline ternary compositions. 3.4. N&l-l&O-C02 The most extensive PV7’X dataset for this ternary system, about 5000 experimental data points covering temperature range from about 200-560°C and pressure range from 0 to 3000 bar, has been reported by Gehrig ( 1980). Note that his
original data need 0.4-2.98 correction (depending on temperature) in volume because of thermal expansion of aparatus. Since this is the only comprehensive PV7X dataset in this T-P range, we can only roughly estimate its uncertainty. The binary HZO-NaCl density data reported by Gehrig (1980) agree with densities interpolated from data reported by Bodnar (1985) witbin about 4% for pressures above 1000 bar. For pressures below 1000 bar, the deviation of the Gehrig (1980) data from those of Bischoff (1980) is about 7% as indicated by Table 4. In addition to these data, Johnson ( 1992) measured isochore locations using synthetic fluid inclusions with .QQ ranging from 0.1-0.5 1 and relative salinities of 6-23.9 wt% around 7000 bar and 900°C. Besides the PV7X data, Takenouchi and Kennedy ( 1965) reported COz solubility data in NaCl aqueous solution from
Equation of state in the system NaCl-H20-CO2
2817
Table 6. Comparisonof experimentalmole volumes with EOS
T(K)
P(bar)
xNcl
XI&o
xcor
VOW
V(DMw)
v(exp)
=mH)
err@Mw)
733
416
.0193
.9789
.0018
40.53
57.94
61.14
-33.71
-5.23
133
435
.0191
.9688
.0121
42.45
56.19
57.88
-26.66
-2.92
713
406
.0186
9439
.0375
45.74
58.62
62.03
-26.26
-5.49
713
403
.0185
.9415
.0400
47.83
60.48
61.14
-21.77
-1.08
703
407
.0183
9303
.0514
44.89
55.31
58.08
-22.72
-4.17
733
517
.0183
9303
.0514
45.88
49.45
51.97
-11.71
-4.85
703
412
.0180
.9146
.0674
51.35
59.46
61.14
-16.02
-2.75
733
402
.0324
9463
.0213
48.22
66.20
66.24
-27.20
-.OS
743
457
.0324
.9463
.0213
44.31
56.30
56.05
-20.94
.45
713
400
.0317
.9252
.0431
44.97
58.56
57.06
-21.19
2.62
763
403
.0714
.9259
.0027
39.22
IO.96
71.33
-45.01
-.52
.8677
.0654
42.86
53.00
56.05
-23.53
-5.43
713
423
The volume are
0569
in cm3/mo1e. v(BH),v(DMW) are the mole volumes calulated by the EOS of
Bowers and Helgeson (1983a) and by the EOS of this study,respectively.v(exp) is experimental mole volume By Gehrig (1980). en=(vm
- v,,).Ioo/v,.
300 to 400°C. Recently, Kotelnikov and Kotelnikova ( 1990) and Frantz et al. ( 1992) measured immiscibilities using synthetic fluid inclusions. The data of Frantz et al. ( 1992) range from 500 to 700°C and 1000-3000 bar. Except for the diagram at 600°C and 3000 bar, all the others have sufficient data to delineate the immiscibility boundaries and tie lines. The data of Kotelnikov and Kotelnikova ( 1990) covers a temperature range from 400 to 800°C and pressure range from 1000 bar to 2000 bar. We were unable to delineate the phase boundaries from this dataset except in the cases of 600 and 800°C at 2000 bar. The boundaries of the immiscibility at these temperatures are consistent with those of Frantz et al. (1992). These two datasets provide important insights into the phase conditions of this system under high T-P conditions. Useful data were also reported by Joyce and Holloway ( 1993 ) . They measured the activity of water in the ternary system using fH2and fs buffers. Based on the measured equilibrium activity-composition relation, they drew tie lines at 850°C and 2000 bar.
There are ten ternary parameters (see Table 5) to be evaluated. If all the ternary interaction parameters are equal to 1.O, it implies that the ternary interactions are negligible, and the ternary properties can be predicted on the basis of the three binary systems. However, our test indicates that ternary interaction parameters are indispensable for the reliable prediction of either phase behavior or volumetric properties, no matter how the binary parameters are adjusted. It was found that all the &&‘s can be set equal to each other with little effect on fitting. This is also true for all the cijWm’s. Therefore, only three ternary parameters as a function of temperature (7 coefficients in total) (see Table 5) need to be adjusted. We evaluated the three ternary parameters based on the 2547 data points (calibrated) of Gehrig (1980), Takenouchi and Kennedy ( 1965). and Frantz et al. ( 1992). These data fall into the T-P range below 700°C and 3000 bar. In order to test the extrapolation of the EOS, we reserve the data of Johnson ( 1991), Joyce and Holloway ( 1993), and Kotelnikov and Kotelnikova ( 1990)) which cover T-Prange up to 950°C and
Table 7. Predictionof Molar Volume (cc/mole) at High Temperaturesand Pressures v(exp)’
v(EOs)*’
.1870
27.61
21.92
.2800
30.78
30.81
.4866
.4890
35.60
34.56
~5483
.2900
29.96
29.94
T(C)
p(b=)
x(NaCl)
x(Hz0)
938
1458
.0410
.7720
930
6600
.0352
.6848
924
6800
.0244
940
7400
.0617
x(Q)
* The exp&mcntal data arc from Johnson (1992) ** calculated mole volume (cm3/mo1e)by the BOS of this study.
Z. Duan, N. Msller, and J. H. Weare
2878
500
Table 8. The Excess Volume’ (cc/mole) TK)
P(bar)
V,,
V,
400
500
49.73
6.48
400
1000
34.89
1.35
400
zoo0
28.98
0.39
500
500
73.05
23.17
500
loo0
41.79
4.65
5Oo
zoo0
31.21
0.19
700
500
118.47
7.04
700
loo0
60.84
9.52
700
zoo0
38.00
2.4
700
5ooo
27.53
-0.08
Pz2000 bar
VW
450
I
* V,,=vhx -
O.~WWZ-~.~VN,CI-~,O
400
I
0:
D
I
0.1
0.2 xyo 3
0.3
0.4
FIG. 10. The P-Tboundaries for the reaction 3 dolomite + 2 quartz + Hz0 = talc + 3 calcite + 3C& in the absence of NaCl (dashed line) and with the addition of 0.1 mole fraction of NaCl (solid line).
7500 bar. As shown below, the EOS is valid over a much broader T-P range than the range for the parameter evaluation.
tithxt.~~h~~~=~.~
4. COMPARISON WITH EXPERIMENTAL DATA 1.0
The reliability and accuracy of an EOS must be determined by comparison with experimental data. Here, we demonstrate the capability of this EOS to predict both phase equilibria (or immiscibilities) and volumetric properties (PVTX) in the ternary system. Figure 2a,b compares the EOS calculation of the liquidvapor equilibria with experimental data at 300 and 350°C respectively. In this figure, the NaCl concentration is not shown on the vapor side because it is so small. The figure
0.6
0.2
0.4 Go
0.6
0.6
1.0
P = 1000 bar
660%
o-05i7cc-9 @I
xyo
.
0.4 XYO
0.6
1.0
1.0 0.6 0.6
a, 0.4
0.0
0.2
0.6
1.0
FIG. 9. (a)-(c) The activities of Hz0 and CO2 at high temperatures and pressures. The cross bars are the experimental measurements of Joyce and Holloway (1993). The curved solid lines are the calculation of this EOS. The diagonal solid lines represent ideal mixing.
FIG. 11. The phase diagram of the system NaCl-H,O-CQ at various temperatures and constant pressure of loo0 bar. The part below 300°C is calculated from the EOS of Duan et al. ( 1992b).
Equation of state in the system NaCI-H*O-CO2
clearly demonstrates that the predictions of this EOS are within experimental accuracy under the conditions shown except near the critical range. It is interesting to note from these figures that the extent of immiscibility can be considerably increased over that of the CO*-Hz0 binary by the addition of NaCl. The accuracy of this EOS in the prediction of phase equilibria (immiscibilities) is further shown by Figs. 3, 4, 5, 6, and 7. Figure 3 shows the close agreement of the prediction of phase coexistence measurements of Frantz et al. ( 1992). Figure 3a,b (see above) indicates that the immiscibility fields decrease with increasing pressure for a given temperature. The diagram at 800°C and 2000 bar of Kotelnikov and Kotelnikova ( 1990), given by Fig. 4, is well predicted by our EOS. Although we did not use any data above 700°C and 3000 bar in the parameterization, the immiscibility at 930°C and 7500 bar are. well predicted as compared with the synthetic fluid inclusion measurement by Johnson ( 1991) (see Fig. 5). The data of Johnson ( 1991) are not sufficient to determine the tie lines. The tie lines between vapor-liquid phase equilibrium established by Joyce and Holloway (1993) are shown in Figs. 6 and 7. We show very good agreement with their data at 850°C and 2000 bar (Fig. 6). In Fig. 7, the tie line measured by Joyce and Holloway ( 1993) is in general agreement with our EOS. However, the schematic phase boundary they drew shows a substantially larger immiscibility field. Their data appear to be insufficient to draw this boundary. Figure 8a-d displays the comparison of volumetric data with the EOS of this study for systems of various compositions. In these figures, the nearly straight lines are the predicted isochores, the dashed lines are predicted phase boundaries, and the solid dots are the experimental PVT data of Gehrig ( 1980). It can be seen that the EOS is very close to the experimental data (within an error of about 6-796 in volume) under various conditions. Table 6 indicates that the EOS of Bowers and Helgeson ( 1983a) has much larger errors. The errors in the low pressure range will lead to big errors in the evaluating fugacities or chemical potentials. Because NaCl is treated as ion-pair molecules in the EOS and it partially dissociates below 35O”C, the accuracy decreases slightly below 350°C. Although the parameters in this EOS are evaluated from data below 700°C and 3000 bar, the volume measurements over 920°C and 7000 bar of Johnson ( 1992) are accurately predicted (see Table 7). 5. PREDICTION OF PROPERExcess volumes, activities, isochores, and phase equilibria can be determined from the EOS. All these properties are important in the understanding of fluid behavior under various geological conditions.
2879
We have previously discussed the excess volume in the C&COz-H20 system (Duan et al., 1992b) and shown that it can be a large percentage of the total volume. In the NaCl-Hz0 system, the excess volume can be both very negative and positive. For example, at 400°C and 1000 bar, the excess volume of the system O.lNaCl + 0.9Hz0 is -47.9 cubic centimeter (cc) when the total volume is 23.1 cc. The accuracy of the ideal geometric mixing approach of Brown and Lamb ( 1989) can be assessed by calculating the excess volume defined as v:, = &niX- xc@&& - (1 - xcl&)+&cI-H~,
(37)
where vti, is the molar volume of the ternary mixed system and VN~CJ-H~ is molar volume of the binary under the same T-P condition and same xN&xHIO ratio. It can be seen from Table 8 that the excess volume amounts to about 7-30% of the total volume for pressures below 2000 bar, and about O5% for pressures above 2000 bar. This implies that the approach (see above) of Brown and Lamb ( 1989) may give approximate result for pressures above 2000 bar, but incorrect results for pressures below 2000 bar. 5.2. Activities The activity of a species
i is
U<=
defined as
Xf4i/$p,
(38)
where 4p is the fugacity coefficient of species i in its pure state. The equations for calculating fugacity coefficients are listed in the Appendix. Comparison of the calculated activities in the binary H20-CO2 with the data of Joyce and Holloway ( 1993). as shown in Fig. 9, indicates that our calculations are in good agreement with experimental data except at the waterrich end. The activity measurements in the ternary NaClH,O-CO* by Joyce and Holloway ( 1993) enabled them to draw a tie line between liquid and vapor phase equilibrium. This tie line is well predicted by our EOS as shown in Figs. 6 and 7. Note that the data of J + H were not used in the evaluation of the parameters. As stated before, adding NaCl in the H20-CO2 system can dramatically change the activities of both Hz0 and C02. For example, at 450°C and 2000 bar, the fugacity coefficients of Hz0 and CO* in the system 0.6H20 + 0.4C02 are 0.316 and 2.404, respectively. However, adding 0.1 mole fraction of NaCl and keeping the Hz0 to CO2 ratio constant, these fugacity coefficients change to 0.222 and 4.607, respectively. This change in activity has a substantial effect on alteration reactions. For example, consider the decarbonation and dehydration reaction: 3CaMg(COs)2(dolomite)
+ 4SiO,(quartz)
+ Hz0
= Mg&,O&OH)z(talc) 5.1. Excess Volume
+ 3CaCO,(calcite)
The excess volume is defined as: ” VU =
l&j,
-
x
XjVi.
(36)
+ 3C02
(39)
in the system CaO-MgO-SiOz-HzO-CO* (Bowers and Helgeson, 1983b). Adding 0.1 mole fraction NaCl relative to NaCl + Hz0 + CO*, the stability field of the minerals will shift substantially as shown in Fig. 10.
2. Duan, N. Mailer, and J. H. Weare
2880
5.3. Calculation of Isochores, Homogenization Temperatures, Pressures, and Immiscihilities Using microthennometric
technique together with Raman spectrometry analyses, it is possible to find out the total composition and total homogenization temperatures (Ramboz et al., 1985; Williams-Jones and Ferreira, 1989; Diamond, 1990). According to the composition analyzed, a constant composition diagram with phase relations and isochores can be calculated. This kind of diagram determines the homogenization pressures (internal pressure) for a given homogenization temperature. With the known temperature, pressure, and compoaitiuu, the volume can be calculated. Isochores can be. calct&ed as needed. Such calculations are illustrated by Fig. 8a-d. The curved dashed lines in these figures are phase boundaries. This boundary also represents hom~)genization T-P aye. P;bove this curve. the system is homogeneous. Below this curve, the fluid separates into liquid and vapor phase. The compositions of the liquid and vapor phase can be determined from the EOS. The end of these dashed lines should be close to critical region. The nearly straight lines are isochores. The immiscibility can be better illustrated by a three dimension phase diagram. Such a diagram can be calculated from the EOS. Figure 11 is a constant pressure diagram show-
ing the phase relations under varying temperatures. It can be seen that the immiscibility field is minimal around 400°C. Above or below this temperature the immiscibility field expands. The dashed line A-B connects the critical points of various temperatures. Above 640°C, there are no critical points. The dashed straight lines are tie-lines representing liquid-vapor coexistence. The tie lines indicate that very highly saline brines may result from phase separation under high temperatures. More details on the relationship between the immiscibility and mineralization will be discussed in a separate publication (Hu et al., 1995). thank Drs. A. Anderko, K. S. Pitzer, and John Wheeler for valuable discussions. This work has been supported by funds from the Department of Energy: DE-FGO7-931D13247, University Energy Research Group, Central Canada Potash, and Unocal Science and Technology Division. Drs. I.-M. Chou, M. Sterner, R. Bodnar, and M. McKibben are acknowledged for their constmctive reviews.
Acknowledgmenrs-We
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Camahan N. F. and Starling K. E. ( 1969) Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51,635-636. Crawford M. L. ( 1981) Phase equilibria in aqueous fluid inclusions. Mineral. Assoc. Can. Short Course Handb. 6,75-
100.
Diamond L. W. ( 1990) Fhrid inclusion evidence for P-V-T-X evolution of hydrothermal solutions in late alpine gold-quartz veins at Rnr~cnn. V-1 d’Ayas, Northwest Italian Alps. Amer. J. Sci. 290, 912-958.
Dimitrelis D. and Prausnitz 1. M. ( 1986) Comparison of two hardsphere reference systems for perturbation theories for mixtures. Fluid Phase Equilibria
31, l-21.
Duan Z., Msller N., and Weare J. H. (1992a) An equation of state for the CH4-C02-H20 system: 1. Pure systems from 0 to 1000°C and 0 to 8000 bar. Geochim. Cosmochim. Acta S6,2605-2617. Duan Z., Meller N., and Weare 1. H. ( 1992b) An equation of state for the CI&-Ca-Hz0 system: Il. mixtures from 50 to 1000°C and from 0 to 1000 bar. Geochim. Cosmochim. Acta 56, 26192631.
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Editorial
handling: M. A. McKibben
REFJZRENCES Alston R. B., Kokolis G. P., and James C. F. ( 1985) COr minimum miscibility pressure: A correlation of impure CO, streams and live oil system.Soc. Pet. J. 25,268-274. Anderko A. and Pitzer K. S. ( 1993) Equation of state representation of phase equilibria and volumetric properties of the system NaCIHz0 above 573 K. Geochim. Cosmochim. Acta 57, 1657- 1680. Bischoff J. L. ( 1980) Geothermal system at 21 “N, East Pacific Rise: Physical limits on geothermal fluid and role of adiabatic expansion. Science 207, 1465 - 1469.
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2881
(A5)
where
‘(2)
aE
+--+_-
aF ax,’
(A61
where D, E, and Fare given by Eqns. 6-9 and 3E9 7
-=-
a0
a $ > -=( aE
-=
3: (1 -9)
(A7)
(1 -T)’
3:’
3E2 FZ
++$ln(l-n),
+(l
(A81
aF
2E’r) 7
Z$ln(l
+(lAPPENDIX
a)?
ax,
aE
a0
CALCULATION OF FUGACITY COEFFICIENTS
ax,= aE
A few errors in the equations of Anderko and Pitzer ( 1993) are corrected here. The fugacity coefficient Qi is given by:
ui*
-r)).
(A9) (AlO)
2
ax,=aF -&=u:.
(AlI
(A121
The dipolar contribution is given by where (pi- pj. ) is the difference between the chemical potential of component i in the real system and that in the ideal gas state. It is given by the sum of the hard-sphere, dipolar, and perturbation con-
Ac(idip_ RT
(A131
(AZ) The derivatives of A2 and A, with respect to the number of moles of component i are
The hard-sphere contribution is expressed as
+z-
ahd FT =
3DE Ff)-F 1-r)
E’
E’ Fz +(l+
1,
(A3)
9),
(A4)
2. Duan, N. Msller, and J. H. Weare
2882 where
x (1 +
Cd?) +
--1 a(n*u) = 2 i xja,, n 84 j_,
cg)* + C6TjJ)
+ (1 + c,q + cg2 + c&Cc,
+ 2~5~ + 3c.&l,
(A17)
n
X Xjby
acns, ,-I -=ani
2v
’
where b, is defined by Eqn. 17. The perturbation contribution to the chemical potential is
(A181
1 B(n%cb) --= n2 Chi
3 i
i
xj-G(ac)&ijk~
(A2’3)
(AZ])
j-l t-l
(A22)